The rabbits eat a lot less of the expensive pellets when I free feed hay. I like to give my rabbits variety. I have given them mown grass hay, real hay bale from the feed store, straw bale from the store and hay from a neighbor who makes his own hay from cutting a field full of all kinds of random plants.
In order of preference, they like 1) mixed hay 2) straw 3) grass 4) hay bale. Since I got a giant roll of the mixed hay, that is going to be what they have for the foreseeable future. They seem to like the heavier, chewier, stick type stuff more than the softer hays. They also like dried leaves.
I also like feeding them hay because it falls to the floor and makes walking nicer, as well as soaking up some of the urine. I have chickens that come in and turn the hay and manure over a couple times a day. They also eat all the fallen grain/pellets.
If you have room for it, a farmer might sell a 'broken' roll of hay cheap, since it's hard to transport LOL (that's what I got)
Liz